1. Field of the Invention
The present invention relates to a belt drive controlling device for controlling drive of a belt which is rotated while supported by plural rollers. In addition, the present invention also relates to a belt device, which transports a material using a belt and the belt drive controlling device, and to an image forming apparatus which produces visual images using a belt and the belt device.
2. Discussion of the Background
Specific examples of apparatuses using a belt device, which transports a material using a belt supported by plural rollers, include image forming apparatuses, which produce visual images using a photoreceptor belt on which a toner image is formed, an intermediate transfer belt to which the toner image is transferred, and/or a feeding belt for feeding a receiving material to transfer the toner image thereon. It is necessary for such image forming apparatuses to precisely control drive of the belt(s) in order to produce high quality images.
Particularly, in direct-transfer type tandem color image forming apparatuses which can produce images at a high speed while having a small size, it is very important to precisely control drive of a feeding belt for feeding a receiving material. In such tandem color image forming apparatuses, a sheet of a receiving material is fed by a feeding belt along plural color image forming units which produce different color toner images so that the different color toner images are transferred onto the receiving material sheet one by one, resulting in formation of a combined multi-color image on the receiving material sheet. The thus formed combined multi-color image is then fixed to the receiving material sheet, resulting in formation of a fixed color image (such as full color images).
FIG. 1 is a schematic view illustrating the image forming section of a direct-transfer type tandem image forming apparatus. The direct-transfer type tandem image forming apparatus will be explained in detail by reference to FIG. 1.
The image forming apparatus includes four image forming units 18K, 18C, 18M and 18Y, which form black, cyan, magenta and yellow toner images, respectively and which are arranged one by one in such a direction that a sheet S of a receiving material is fed. The image forming units 18K, 18C, 18M and 18Y respectively include photoreceptor drums 40K, 40C, 40M and 40Y, on each of which an electrostatic latent image is formed by a charger and a laser light irradiation device. In each of the image forming units, the electrostatic latent image is developed with a developing device, resulting in formation of a toner image on the photoreceptor drum 40.
The thus prepared toner image is transferred by a transfer roller 62 onto the receiving material sheet S, which is fed by a feeding belt 10 while electrostatically adhered to the belt 10. Thus, four color toner images (black, cyan, magenta and yellow toner images) are transferred onto the sheet S while overlaid, resulting in formation of a combined multiple color toner image. The combined color toner image is then heated and pressed by a fixing device 25, and thereby a fixed full color image is formed on the sheet S. In this regard, the feeding belt 10 is rotated by a driving roller 15 while stretched at a proper tension by the driving roller 15 and a driven roller 14.
The driving roller 15 is driven by a driving motor (not shown) so as to rotate at a predetermined revolution, and thereby the feeding belt 10 is allowed to make an endless movement. The receiving material sheet S is timely fed toward the image forming units 18 so that the color toner images are transferred to proper positions of the sheet S. Since the sheet S is fed by the feeding belt 10, the sheet is fed along the image forming units 18 (in order of 18K, 18C, 18M and 18Y) at the same moving speed as that of the feeding belt 10.
In such an image forming apparatus, unless the moving speed of the sheet S (i.e., the moving speed of the feeding belt 10) is even, a misalignment problem in that color toner images are transferred to improper positions of the sheet S, resulting in formation of misaligned color toner images is caused. When such a misalignment problem is caused, for example, a problem in that a combined color line image, which should be formed by precisely superimposing two or more different color line images, looks blurred because the different color line images are formed while separated from each other without superimposed, or a problem, in that a white portion is formed around a black image formed in a background image which consists of overlaid plural color images, occurs.
FIG. 2 is a schematic view illustrating another tandem image forming apparatus, which uses an intermediate transfer belt. In this image forming apparatus, the color toner images, which are formed on the photoreceptors 40 of the image forming units 18, are transferred by the transfer rollers 62 to an intermediate transfer belt 11 one by one so as to be superimposed, resulting in formation of a combined multiple color toner image on the intermediate transfer belt 11. The combined multiple color toner image is then transferred onto the receiving material sheet S. Similarly to the image forming apparatus illustrated in FIG. 1, the misalignment problem is caused unless the moving speed of the sheet S (i.e., the moving speed of the intermediate transfer belt 11) is even.
As illustrated in FIG. 2, the image forming apparatus includes a secondary transfer belt 24, which is rotated while stretched by two rollers, three support rollers 14, and 16, a cleaner 9 configured to clean the intermediate transfer medium 11, a pair of registration rollers 49 configured to stop and timely feed the sheet S, and the fixing device 25 configured to fix the toner images onto the sheet S.
In the above-mentioned tandem image forming apparatuses and other image forming apparatuses which use a feeding belt configured to feed a receiving material sheet, and/or an image bearing belt member (such as photoreceptor belts and intermediate transfer belts) configured to bear a toner image, a banding problem in that an uneven density portion like a band (like stripe images) is periodically formed on a colored background due to uneven feeding of the receiving material sheet and/or the image bearing belt member. Specifically, when a toner image is transferred to a belt or sheet moving at a relatively high moving speed, the transferred toner image is extended in the moving direction of the belt or sheet, resulting in formation of an image having a relatively low image density. In contrast, when a toner image is transferred to a belt or sheet moving at a relatively low moving speed, the transferred toner image is shrunk in the moving direction of the belt or sheet, resulting in formation of an image having a relatively high image density. Thus, a banded (stripe) image is formed, i.e., the banding problem is caused. Particularly, human eyes are very sensitive to banded pale color images.
The moving speed of a belt is varied from various causes. One of the causes is the uneven thickness of the belt in the moving direction thereof. For example, when the belt is prepared by a centrifugal method such that a belt prepared by centrifugal force using a cylindrical die is then baked, a problem in that the thickness of the resultant belt varies in the circumferential direction thereof often occurs. When such a belt as having uneven thickness is used, the moving speed of the belt varies. Specifically, when a relatively thick portion of the belt is contacted with a driving roller, the moving speed of the belt is relatively fast. In contrast, when a relatively thin portion of the belt is contacted with the driving roller, the moving speed of the belt is relatively slow. Thus, the moving speed of the belt varies. The reason therefor is as follows.
FIG. 3 is a graph showing variation of the thickness of a belt in the circumferential direction thereof. Specifically, the belt is used as the intermediate transfer belt 11 of the image forming apparatus illustrated in FIG. 2.
The graph illustrates variation of the thicknesses of the belt in the circumferential direction thereof, i.e., the relationship between the positions of the belt in the circumferential direction (plotted on the X-axis) and the thickness of the positions (plotted on the Y-axis). In this regard, one circuit of the belt is represented as 2π radian. In addition, the deviation from the average thickness (i.e., 100 μm) is plotted on the Y-axis, and the average thickness is represented as the zero point in FIG. 3.
Hereinafter, the variation of thickness of a belt in the circumferential direction per one circuit is referred to as a belt thickness variation.
In this application, the terms of “belt thickness unevenness” and “belt thickness variation” are defined as follows. The term of “belt thickness unevenness” means distribution of the thicknesses of the belt measured with a thickness meter, and such belt thickness unevenness is present in both the circumferential direction (i.e., feeding direction) and the width direction (roller axis direction) of the belt. In contrast, the term of “belt thickness variation” means distribution of the thicknesses of the belt, which influences the belt feeding speed and/or the angular velocity of the driven roller and which causes variation in rotation of the belt and has the same cycle as the rotation cycle of the belt.
FIG. 4 is a schematic view illustrating a portion of a belt looped around a driving roller when the belt and driving roller are observed from the direction of the axis of the roller. The moving speed of a belt 103 changes depending on a pitch line distance (hereinafter referred to as a PLD) between the surface of a driving roller 105 and a belt pitch line indicated by a dotted line in FIG. 4.
When the belt 103 is a uniform single-layered belt and the absolute value of the expansion ratio of the outer surface of the belt is almost the same as that of the contraction ratio of the inner surface of the belt, the PLD is the same as the distance between the center line of the belt in the thickness direction and the inner surface of the belt (i.e., the surface of the driving roller 105). Thus, in the case of a single-layered belt, the PLD is substantially proportional to the thickness of the belt. Therefore, the moving speed of the belt 103 changes depending on the belt thickness variation.
However, when the belt is a multi-layered belt, which is, for example, made of a hard layer and a soft layer, the PLD is a distance between the surface of the driving roller 105 and the belt pitch line, which is different from the centerline of the belt 103. In addition, the PLD changes depending on the belt contact angle, at which the surface of the roller 105 is contacted with the inner surface of the belt 103.
The pitch line distance PLD of a belt is represented by the following equation (1):PLD=PLDave+ƒ(d)  (1)wherein PLDave represents the average value of the PLD per one circuit of the belt; and ƒ(d) represents a function representing the variation of the PLD, wherein d represents the position of a point of the belt determined on the basis of the reference point of the belt, i.e., the phase of the point determined when the one circuit of the belt is defined as 2π radian.
In the case of a single-layered belt having an average thickness of 100 μm, the PLDave is 50 μm as can be understood from FIG. 4.
The function ƒ(d) is highly correlated with the belt thickness variation illustrated in FIG. 3, and is a periodic function having a period corresponding to one circuit of the belt. When the PLD of the belt varies in the circumferential direction thereof, the ratio of the belt moving speed (or belt moving distance) to the angular velocity (or rotation angular displacement) of the driving roller varies, and/or the ratio of the angular velocity (or rotation angular displacement) of the driven roller to the belt moving speed (or belt moving distance) varies.
The relationship between the belt moving speed V and the angular velocity ω of the driving roller 105 is represented by the following equation (2):V={r+PLDave+kƒ(d)}ω  (2)wherein r represents the radius of the driving roller 105, and k represents the PLD variation effective coefficient, which represents the degree of the influence of the PLD variation ƒ(d) on the moving speed (or moving distance) of the belt 103 or the angular velocity (or rotation angular displacement) of the driven roller.
In this regard, the PLD variation effective coefficient k changes depending on the contact state of the belt 103 with the driving roller 105, and the belt contact angle mentioned above.
In equation (2), {r+PLDave+kƒ(d)} is hereinafter referred to as the effective roller radius, and the constant portion (r+PLDave) of the effective roller radius is hereinafter referred to as the constant effective roller radius R. In addition, ƒ(d) is hereinafter referred to as the PLD variation.
It can be understood that since equation (2) includes the PLD variation ƒ(d), the relationship between the belt moving speed V and the angular velocity ω of the driving roller 105 varies. Specifically, even when the driving roller 105 is rotated at a constant angular velocity (i.e., ω is constant), the moving speed of the belt 103 changes depending on the PLD variation ƒ(d).
Specifically, for example, when a relatively thick portion of a single-layered belt is located on the surface of the driving roller 105, the PLD variation takes on a positive value, and thereby the effective roller radius is increased. Therefore, even when the driving roller is rotated at a constant angular velocity, the moving speed of the belt 103 is increased.
In contrast, when a relatively thin portion of a single-layered belt is located on the surface of the driving roller 105, the PLD variation takes on a negative value, and thereby the effective roller radius is decreased. Therefore, even when the driving roller is rotated at a constant angular velocity, the moving speed of the belt 103 is decreased.
Thus, even when the driving roller is rotated at a constant angular velocity, it is impossible to make the belt moving speed constant due to the PLD variation ƒ(d). In other words, it is impossible to control drive of the belt 103 so as to be the target speed only by controlling the angular velocity of the driving roller 105.
In addition, the relationship between the belt moving speed and the angular velocity of a driven roller is similar to the above-mentioned relationship between the belt moving speed V and the angular velocity ω of the driving roller 105. Specifically, when the angular velocity of a driven roller is measured with a rotary encoder or the like, the belt moving speed V can be determined from the angular velocity of the driven roller using equation (2).
More specifically, for example, when a relatively thick portion of a single-layered belt is located on the surface of the driven roller, the PLD variation takes on a positive value, and thereby the effective roller radius is increased. Therefore, even when the belt is rotated at a constant moving speed (i.e., V is constant), the angular velocity of the driven roller is decreased.
In contrast, when a relatively thin portion of a single-layered belt is located on the surface of the driven roller, the PLD variation takes on a negative value, and thereby the effective roller radius is decreased. Therefore, even when the belt is rotated at a constant moving speed, the angular velocity of the driven roller is increased.
Thus, even when the moving speed of the belt 103 is constant, it is impossible to make the angular velocity of the driven roller constant due to the PLD variation ƒ(d). In other words, it is impossible to control the belt moving speed of the belt 103 at the target speed on the basis of the angular velocity of the driven roller.
In attempting to control drive of a belt while considering the PLD variation ƒ(d), several proposals have been made. For example, published unexamined Japanese patent application No. (hereinafter referred to as JP-A) 2000-310897 (i.e., Japanese patent No. 3,658,262, corresponding to U.S. Pat. No. 6,324,355) discloses a technique in that a belt, which is prepared by a centrifugal molding method and which tends to have a sine-wave form PLD variation in the circumferential direction thereof, is set in an image forming apparatus after measuring the profile (unevenness in thickness) of the belt, and storing the profile data in a flash ROM to control the moving speed of the belt in the apparatus on the basis of the profile data. In this image forming apparatus, a reference mark is formed at a home position on the belt so that the phase of the profile data is matched to that of the unevenness of thickness of the belt. In this technique, a position of the belt is determined on the basis of the reference mark, and then controlling of drive of the belt is performed by canceling the variation of the belt moving speed due to the belt thickness variation.
However, it is necessary for this technique to measure the profile (unevenness in thickness) of the belt with a high precision thickness meter. Therefore, the manufacturing costs of the belt and image forming apparatus seriously increase. In addition, when the belt is replaced with a new belt, it is necessary to input the profile data of the new belt to the image forming apparatus. Further, in the apparatus, the data of the belt thickness unevenness are used instead of the data of the PLD variation ƒ(d), and therefore it is difficult to precisely control drive of a multi-layered belt, although it may be possible to precisely control drive of a single-layered belt.
JP-A 10-78734 (i.e., Japanese patent No. 3,186,610, corresponding to U.S. Pat. No. 5,995,802) discloses a technique in that detection pattern images are formed on a belt, and the pattern is detected with a detection sensor to detect the periodic variation of the belt. In this image forming apparatus, controlling rotation of a driving roller is performed such that the periodic variation of the belt moving speed due to the belt thickness variation is canceled to control driving of the belt.
It is necessary for the image forming apparatus to form detection pattern images in a range corresponding to at least one circuit of the belt. Therefore, a large amount of developer (toner) is used therefor, resulting in increase of the running costs. In addition, in order to precisely detect the variation of the belt moving speed, detection pattern images have to be formed in a range corresponding to plural circuits of the belt to obtain the averaged variation data of the belt moving speed. Therefore, a larger amount of developer (toner) is used therefor, resulting in serious increase of the running costs.
The present inventors and other inventors disclose a belt drive controlling device in JP-A 2004-123383. In the belt drive controlling device, the rotation angular displacement or angular velocity of a driven support roller is detected, and then the alternating component of the of the angular velocity of the driven roller, which has a frequency corresponding to the periodic thickness variation of the belt, is extracted from the detected data. The amplitude and phase of the thus determined alternating component correspond to those of the periodic thickness variation of the belt. In addition, controlling is performed on the basis of the information on the amplitude and phase of the alternating component such that the rotation angular velocity of a driving roller is decreased (or increased) when a relatively thick (or thin) portion is located on the driving roller. By using this technique, the belt can be driven so as to have the predetermined moving speed without being influenced by the variation in thickness of the belt in the circumferential direction thereof. In addition, it is not necessary for this technique to measure the thicknesses of the belt in the manufacturing process thereof to determine the thickness variation, and therefore increase of the manufacturing costs can be avoided. Further, it is not necessary to input such profile data as mentioned above to the image forming apparatus when the belt is replaced with a new belt. Furthermore, it is not necessary to form such detection pattern images as used for the technique disclosed in JP-A 10-78734, resulting in saving of toner.
However, in the belt drive controlling device, the belt thickness variation is considered as a sine (or cosine) periodic function. Therefore, it is necessary to previously determine the belt thickness variation of the entire belt. Specifically, it is necessary to previously determine whether the frequency component included in the belt thickness variation includes only a fundamental frequency component having a period corresponding to one circuit of the belt or a combination of the fundamental frequency component and a high-order frequency component. In addition, when a seam belt having a thick seam is used, abnormal belt thickness variation tends to be caused. In this case, it is difficult to approximate the belt thickness variation at a periodic sine function, and therefore control error may be committed by this method.
Further, in JP-A 2006-264976, the present inventors propose a belt drive controlling device, which improves the belt drive controlling device disclosed in JP-A 2004-123383. The device controls drive of a belt which is rotated while stretched by plural support rollers including a driving roller configured to drive the belt and a driven roller which is rotated by the belt. The device controls drive of the belt by the following method. Specifically, the method includes obtaining information on rotation angular displacement or rotation angular velocity of two support rollers, which have different diameters or which have different properties such that influences of their PLDs on the belt moving speed and their angular velocities are different from each other; and then performing controlling according to the thus obtained information such that the variation of the belt moving speed due to the variation of the PLD in the circumferential direction of the belt is minimized.
In the device mentioned above, the method of calculation of a control parameter to minimize the variation of the belt moving speed (i.e., the PLD variation determining method) is as follows. Specifically, two pieces of rotation variation information, which are included in the rotation information of one or both of the support rollers and which have different phases, are subjected to an addition treatment in which a delay time representing the time needed for the belt to move from one of the rollers to the other roller and a gain of the two rollers are added. In addition, a second addition treatment is performed on the basis of the results of the first addition treatment. Thus, the addition treatment is repeated n times, wherein n is an integer of not less than 1. In the n-time addition treatment, the gain is G2n−1, wherein G represents the gain in the first addition treatment, and the delay time is T2n−1, wherein T represents the time needed for the belt to move from one of the roller to the other roller.
In the technique, the diameter of the two support rollers has to be different. Namely, there is a limitation on designing the belt feeding device.
Because of these reasons, a need exists for a belt drive controlling device, which can precisely control drive of a belt supported by plural support rollers without any limitation.